pip install scipy

import scipy

from scipy.optimize import minimize
# 定義目標(biāo)函數(shù)
def objective(x):
    return x[0]**2 + x[1]**2
# 初始猜測(cè)點(diǎn)
x0 = [1, 1]
# 使用BFGS算法尋找最小值
result = minimize(objective, x0, method='BFGS')
# 輸出最小值和最優(yōu)參數(shù)
print("最小值:", result.fun)
print("最優(yōu)參數(shù):", result.x)

from scipy.optimize import minimize
# 定義目標(biāo)函數(shù)
def objective(x):
    return x[0]**2 + x[1]**2
# 定義約束條件
constraint = ({'type': 'ineq', 'fun': lambda x: x[0] - 2},
              {'type': 'ineq', 'fun': lambda x: x[1] - 2})
# 初始猜測(cè)點(diǎn)
x0 = [1, 1]
# 使用SLSQP算法進(jìn)行約束優(yōu)化
result = minimize(objective, x0, method='SLSQP', constraints=constraint)
# 輸出最小值和最優(yōu)參數(shù)
print("最小值:", result.fun)
print("最優(yōu)參數(shù):", result.x)

from scipy import stats
# 生成隨機(jī)數(shù)據(jù)
data = np.random.normal(0, 1, 100)
# 計(jì)算均值和標(biāo)準(zhǔn)差
mean = np.mean(data)
std_dev = np.std(data)
# 計(jì)算數(shù)據(jù)的正態(tài)分布擬合參數(shù)
params = stats.norm.fit(data)

from scipy import stats
# 生成兩組隨機(jī)數(shù)據(jù)
data1 = np.random.normal(0, 1, 100)
data2 = np.random.normal(1, 1, 100)
# 執(zhí)行獨(dú)立樣本t檢驗(yàn)
t_statistic, p_value = stats.ttest_ind(data1, data2)
# 輸出
t統(tǒng)計(jì)量和p值
print("t統(tǒng)計(jì)量:", t_statistic)
print("p值:", p_value)

from scipy import stats
# 創(chuàng)建一個(gè)正態(tài)分布隨機(jī)變量
rv = stats.norm(loc=0, scale=1)
# 計(jì)算概率密度函數(shù)的值
pdf_value = rv.pdf(0)
# 計(jì)算累積分布函數(shù)的值
cdf_value = rv.cdf(0.5)

from scipy import signal
# 生成一個(gè)包含噪聲的信號(hào)
t = np.linspace(0, 10, 1000)
signal_data = np.sin(t) + np.random.normal(0, 0.5, 1000)
# 設(shè)計(jì)一個(gè)低通濾波器
b, a = signal.butter(4, 0.1, 'low')
# 應(yīng)用濾波器
filtered_signal = signal.filtfilt(b, a, signal_data)

from scipy import fft
# 生成一個(gè)包含兩個(gè)頻率分量的信號(hào)
t = np.linspace(0, 1, 1000)
signal_data = np.sin(2 * np.pi * 5 * t) + np.sin(2 * np.pi * 10 * t)
# 進(jìn)行快速傅里葉變換
fft_result = fft.fft(signal_data)
# 計(jì)算頻率譜
freq = fft.fftfreq(len(fft_result))
# 提取幅度譜
amplitude_spectrum = np.abs(fft_result)

from scipy import interpolate
# 創(chuàng)建一些示例數(shù)據(jù)點(diǎn)
x = np.array([0, 1, 2, 3, 4])
y = np.array([0, 2, 1, 3, 4])
# 創(chuàng)建線性插值函數(shù)
linear_interp = interpolate.interp1d(x, y)
# 在新的點(diǎn)上進(jìn)行插值
new_x = np.array([0.5, 1.5, 2.5])
interpolated_values = linear_interp(new_x)

from scipy import interpolate
# 創(chuàng)建一些示例數(shù)據(jù)點(diǎn)
x = np.array([0, 1, 2, 3, 4])
y = np.array([0, 2, 1, 3, 4])
z = np.array([[0, 1, 2, 3, 4],
              [4, 3, 2, 1, 0]])
# 創(chuàng)建二維插值函數(shù)
interp2d = interpolate.interp2d(x, y, z, kind='linear')
# 在新的點(diǎn)上進(jìn)行插值
new_x = np.array([0.5, 1.5, 2.5])
new_y = np.array([0.5, 1.5])
interpolated_values = interp2d(new_x, new_y)